Recently, there has been a lot of work on algorithmic phase retrieval.
For example, phase retrieval can be formulated as a low-rank (actually, rank-1) matrix recovery problem [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, and with this formulation, phase retrieval is possible from \(N=O(M)\)  intensity measurements [2]}.
Another approach is to exploit the polarization identity along with expander graphs to design a measurement ensemble and apply spectral methods to perform phase retrieval [8]}, [9]}.
One can also formulate phase retrieval in terms of MaxCut, and solvers for this formulation are equivalent to a popular solver (PhaseLift) for the matrix recovery formulation [10]}, [11]}.
While this recent work has focused on stable and efficient phase retrieval from asymptotically few measurements (namely, \(N=O(M)\) ), the present paper focuses on injectivity and algorithmic efficiency with the absolute minimum number of measurements.
